Celebrated past results have shown that for any strategic-form game, minimizing average external regret for all players leads to a CCE while minimizing average internal regret for all players leads to a CE [1]}.
Many well-known methods exist for minimizing both internal and external regret. For our experiments in external regret minimization, we use Blackwell's regret minimization [2]}, which asks every player to select their next action proportional to how much they regret having not selected that action in the past.
Formally, each player selects action \(a_i \in A_i\)  at timestep \(t+1\)  with probability
\(\Pr (a^{t+1}_i = a_i) = \frac{R^{E,t}_{i, +}(a_i)}{\sum _{a^{\prime }_i \in A_i} R^{E,t}_{i,+}(a^{\prime }_i)}\) 
